Academic and research departments

Biography

My research focuses on the mathematical modelling of biological systems. I joined the University of Surrey as a Lecturer in Mathematics in January 2012. Prior to this I spent four years at Heidelberg University as a postdoctoral fellow, and three and a half years as a postdoctoral researcher at Oxford University. I completed my doctoral research in fluid dynamics in 2004 at the University of Oxford, where I read mathematics as an undergraduate.

Areas of specialism

Biophysics;
Mathematical Biology;
Cancer biophysics

University roles and responsibilities

Admissions Tutor

Affiliations and memberships

London Mathematical Society

Member

Society of Mathematical Biology

Member (Developmental Biology subgroup)

European Society for Mathematical and Theoretical Biology

Member

News

Research

Research interests

I am interested in using mathematical and computational approaches to solve a broad range of problems in developmental biology, tissue morphogenesis and cancer modelling. A particular research focus is on the cell as a physical object, incorporating an understanding of the role of mechanical forces into models of biological processes. I draw on a diverse range of concepts in pursuing this research ranging from population modelling to the theories of fluid dynamics and elasticity theory. Currently ongoing projects include work on tissue self-organization, mechanical regulation of growth and cellular contractility.

Research projects

Open positions

PhD positions available within the group - please do get in touch.

Mechanobiology

The importance of the cell as a physical object and of mechanical interactions in directing cellular behaviours is now clear. We use mathematical modelling to investigate how physical forces internally generated within cells can direct cellular behaviour through mechanotransduction - and in particular on the role of cell-substrate (in vitro) and cell-ECM interactions in this process.

PKPD modelling for cancer treatments

Quantitative systems pharmacology is being increasingly recognised as being of high value in the pharma sector. We here focus on PKPD models of drug effects in tissue within the context of mathematical oncology. (A collaboration with AstraZeneca)

Mathematical models of morphogenesis for tissue engineering

In many context, healthy tissue function is dependent on structure. The question of how tissues develop their shape and size underpins the field of tissue morphogenesis. By considering how growth and active cellular behaviours can generate force and tissue adaption we investigate this process in a range of tissues looking cellular positioning, branching structures, and size control. This has implications for diseases associated with disregulation of morphogenesis and organoid (synthetic tissue) development.

Modelling for biophysical experiment

The range of techniques available for interrogating the biophysics of cells and tissues has exploded over recent years. These new experiments have illuminated the physical nature of cells. We use mathematical modelling of cellular mechanics to inform the interpretation of what these experimental observations could imply for cell cytoskeletal dynamics and force generation. This is particularly important, where cells are seen to interact with each other in multicellular systems so that isolating individual cell behaviours experimentally is difficult.

This paper deals with violent discontinuities in shallow water flows with large Froude number F. On a horizontal base, the paradigm problem is that of the impact of two fluid layers in situations where the flow can be modelled as two smooth regions joined by a singularity in the flow field. Within the framework of shallow water theory, we show that, over a certain time-scale, this discontinuity may be described by a delta shock, which is a weak solution of the underlying conservation laws in which the depth and mass and momentum fluxes have both delta function and step function components. We also make some conjectures about how this model evolves from the traditional model for jet impacts in which a spout is emitted. For flows on a sloping base, we show that for flow with an aspect ratio of O(F?2) on a base with an O(1) or larger slope, the governing equations admit a new type of discontinuous solution that is also modelled as a delta shock. The physical manifestation of this discontinuity is a small ?tube? of fluid bounding the flow. The delta-shock conditions for this flow are derived and solved for a point source on an inclined plane. This latter delta-shock framework also sheds light on the evolution of the layer impact on a horizontal base

In syncytial embryos nuclei undergo cycles of division and rearrangement within a common cytoplasm. It is presently unclear to what degree and how the nuclear array maintains positional order in the face of rapid cell divisions. Here we establish a quantitative assay, based on image processing, for analysing the dynamics of the nuclear array. By tracking nuclear trajectories in Drosophila melanogaster embryos, we are able to define and evaluate local and time-dependent measures for the level of geometrical order in the array. We find that after division, order is re-established in a biphasic manner, indicating the competition of different ordering processes. Using mutants and drug injections, we show that the order of the nuclear array depends on cytoskeletal networks organised by centrosomes. While both f-actin and microtubules are required for re-establishing order after mitosis, only f-actin is required to maintain the stability of this arrangement. Furthermore, f-actin function relies on myosin-independent non-contractile filaments that suppress individual nuclear mobility, whereas microtubules promote mobility and attract adjacent nuclei. Actin caps are shown to act to prevent nuclear incorporation into adjacent microtubule baskets. Our data demonstrate that two principal ordering mechanisms thus simultaneously contribute: (1) a passive crowding mechanism in which nuclei and actin caps act as spacers and (2) an active self-organisation mechanism based on a microtubule network.

This paper presents a biomechanical model for the small pits, called crypts, that line the colon. A continuum approach is adopted, with the crypt epithelium modelled as a growing beam attached to the underlying lamina by cell bonds, which generate tension within the layer. These cell attachments are assumed to be viscoelastic thus allowing for cell progression along the crypt. It is shown that any combination of: an increase in net proliferation (i.e. cell production minus apoptosis), an enlargement of the proliferative compartment, an increase in the strength of the cellular attachment to the underlying lamina, or a change in the rate of cell growth or cell bonding may generate buckling of the tissue. These changes can all be generated by an activating mutation of the Wnt cascade, which is generally accepted to be the first genetic change in colorectal cancer, with subsequent deformation, budding, and crypt fission an observed feature of the adenomatous crypt.

Johnston MD, Edwards CM, Bodmer WF, Maini PK, Chapman SJ(2007)Mathematical modeling of cell population dynamics in the colonic crypt and in colorectal cancer, Proceedings of the National Academy of Sciences of the United States of America104(10)pp. 4008-4013

Epithelial cell layers on soft elastic substrates or pillar arrays are commonly used as model systems for investigating the role of force in tissue growth, maintenance and repair. Here we show analytically that the experimentally observed localization of traction forces to the periphery of the cell layers
does not necessarily imply increased local cell activity, but follows naturally from the elastic problem of a finite-sized contractile layer coupled to an elastic foundation. For homogeneous contractility, the force localization is determined by one dimensionless parameter interpolating between linear and
exponential force profiles for the extreme cases of very soft and very stiff substrates, respectively. If contractility is sufficiently increased at the periphery, outward directed displacements can occur at intermediate positions. We also show that anisotropic extracellular stiffness can lead to force
localization in the stiffer direction, as observed experimentally.

Schwarz US, Dunlop CM(2012)Developmental biology: A growing role for computer simulations, Current Biology22(11)

There is increasing experimental interest in mechanotransduction in
multi-cellular tissues as opposed to single cells. This is driven by a growing awareness of
the importance of physiologically relevant three-dimensional culture and of cell-cell and
cell-gel interactions in directing growth and development. The paradigm biophysical
technique for investigating tissue level mechanobiology in this context is to grow
model tissues in artificial gels with well-defined mechanical properties. These studies
often indicate that the stiµness of the encapsulating gel can significantly alter cellular
behaviours. We demonstrate here potential mechanisms linking tissue growth with
stiµness-mediated mechanotransduction. We show how tissue growth in gel systems
generates points at which there is a significant qualitative change in the cellular stress
and strain experienced. We show analytically how these potential switching points
depend on the mechanical properties of the constraining gel and predict when they
will occur. Significantly, we identify distinct mechanisms that act separately in each of
the stress and strain fields at diµerent times. These observations suggest growth as a
potential physical mechanism coupling gel stiµness with cellular mechanotransduction
in three-dimensional tissues. We additionally show that non-proliferating areas, in
the case that the constraining gel is soft compared with the tissue, will expand and
contract passively as a result of growth. Central compartment size is thus seen to not
be a reliable indicator on its own for growth initiation or active behaviour.

Maintenance and activation of the limited supply of primordial follicles in the ovary are
important determinants of reproductive lifespan. Currently, the molecular programme that
maintains the primordial phenotype and the early events associated with follicle activation
are not well defined. Here we have systematically analysed these events using microscopy
and detailed image analysis. Using the immature mouse ovary as a model, we demonstrate
that the onset of granulosa cell (GC) proliferation results in increased packing density on the
oocyte surface and consequent GC cuboidalisation. These events precede oocyte growth
and nuclear translocation of FOXO3a, a transcription factor important in follicle activation.
Immunolabelling of the TGFb signalling mediators and transcription factors, SMAD2/3,
revealed a striking expression pattern specific to GCs of small follicles. SMAD2/3 was
expressed in the nuclei of primordial GCs but was mostly excluded in early growing follicles.
In activated follicles, GC nuclei lacking SMAD2/3 generally expressed Ki67. These findings
suggest that the first phenotypic changes during follicle activation are observed in GCs, and
that TGFb signalling is fundamental for regulating GC arrest and the onset of proliferation.